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<div class="title">univar_polynomial.h</div>  </div>
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<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#ifndef _UNIVAR_POLYNOMIAL_H</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#define _UNIVAR_POLYNOMIAL_H</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="preprocessor">#include &lt;boost/math/special_functions/fpclassify.hpp&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="preprocessor">#include &lt;boost/math/special_functions/cbrt.hpp&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="preprocessor">#include &lt;boost/math/special_functions/sign.hpp&gt;</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="preprocessor">#include &lt;boost/math/tools/polynomial.hpp&gt;</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="preprocessor">#include &lt;boost/math/tools/roots.hpp&gt;</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;</div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#include &lt;utility&gt;</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;</div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="keyword">namespace </span>bmt = boost::math::tools;</div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="keyword">namespace </span>bmp = boost::math::policies;</div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="keyword">namespace </span>bm = boost::math;</div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="keyword">class </span><a class="code" href="classcVariable.html">cVariable</a>;</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00025"></a><span class="lineno"><a class="line" href="classcUnivarPolynomial.html">   25</a></span>&#160;<span class="keyword">class </span><a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial</a></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;{</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="keyword">public</span>:</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;    <span class="keyword">explicit</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial</a>(std::size_t tolerance = std::numeric_limits&lt;T&gt;::digits)</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;        :m_Tolerance(tolerance)</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    {}</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial</a>(<span class="keyword">const</span> std::vector&lt;T&gt;&amp; coefficients, std::size_t tolerance = std::numeric_limits&lt;T&gt;::digits)</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;        :m_PolyImpl(&amp;coefficients[0], coefficients.size() - 1),</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;         m_Tolerance(tolerance)</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    {</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;        assert(m_PolyImpl[degree()] != 0);</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    }</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial</a>(<span class="keyword">const</span> T* data, std::size_t degree, std::size_t tolerance = std::numeric_limits&lt;T&gt;::digits)</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;        :m_PolyImpl(data, degree),</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;         m_Tolerance(tolerance)</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;    {</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;        assert(m_PolyImpl[degree] != 0);</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;    }</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;    ~<a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial</a>() {}</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    <span class="keywordtype">size_t</span> size()<span class="keyword">const</span></div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;        <span class="keywordflow">return</span> m_PolyImpl.size();</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;    }</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    <span class="keywordtype">size_t</span> degree()<span class="keyword">const</span></div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;        <span class="keywordflow">if</span>(m_PolyImpl.size() == 0)</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;            <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;        <span class="keywordflow">return</span> m_PolyImpl.size() - 1;</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    }</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    <span class="keyword">static</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a> zero()</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    {</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a>();</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    }</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a> <a class="code" href="classcUnivarPolynomial.html#af0fa0596f636515bcab1e2dedc2fde79">derivative</a>()<span class="keyword">const</span>;</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a> primitive()<span class="keyword">const</span>;</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;    <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a> inverse()<span class="keyword">const</span>;</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    std::vector&lt;double&gt; <a class="code" href="classcUnivarPolynomial.html#a0d81e941a048c6ca649dd11d8a4cda8b">realZeros</a>()<span class="keyword">const</span>;</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    std::vector&lt;std::pair&lt;double, double&gt; &gt; <a class="code" href="classcUnivarPolynomial.html#abd186b4aab94bf19bf33796df810785e">plotPoints</a>(<span class="keywordtype">double</span> min, <span class="keywordtype">double</span> max, <span class="keywordtype">double</span> increment)<span class="keyword">const</span>;</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    std::vector&lt;std::complex&lt;T&gt; &gt; complexZeroes()<span class="keyword">const</span>;</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a>&amp; <a class="code" href="classcUnivarPolynomial.html#a3aeaae886ae33ff00e9207847c68deb2">operator%=</a>(<span class="keyword">const</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial</a>&amp; poly);</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a>&amp; <a class="code" href="classcUnivarPolynomial.html#a4158585d1768e886c6802030f6ec128f">operator*=</a>(<span class="keyword">const</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial</a>&amp; poly);</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;    <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a>&amp; <a class="code" href="classcUnivarPolynomial.html#a4158585d1768e886c6802030f6ec128f">operator*=</a>(T num);</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;    <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a>&amp; <a class="code" href="classcUnivarPolynomial.html#a60558f674dbadb2d18e3406f4d45da0e">operator/=</a>(<span class="keyword">const</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial</a>&amp; poly);</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a>&amp; <a class="code" href="classcUnivarPolynomial.html#a60558f674dbadb2d18e3406f4d45da0e">operator/=</a>(T divisor);</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">typename</span> Y&gt;</div>
<div class="line"><a name="l00112"></a><span class="lineno"><a class="line" href="classcUnivarPolynomial.html#a651a710f52fdd21136419d2c6fef5574">  112</a></span>&#160;    T <a class="code" href="classcUnivarPolynomial.html#a651a710f52fdd21136419d2c6fef5574">operator()</a>(<span class="keyword">const</span> Y&amp; value)<span class="keyword">const</span></div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;        <span class="keywordflow">if</span>(0 == size())</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;            <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;        <span class="keywordflow">if</span>(degree() == 0)</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;            <span class="keywordflow">return</span> m_PolyImpl[0];</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;        <span class="keywordflow">return</span> m_PolyImpl.evaluate(value);</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    }</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;    <span class="keywordtype">bool</span> <a class="code" href="classcUnivarPolynomial.html#a54e506b4fac4647cc8aad776ba131940">operator==</a>(<span class="keyword">const</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial</a>&amp; poly)<span class="keyword">const</span>;</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;    std::vector&lt; cUnivarPolynomial&lt;T&gt; &gt; <a class="code" href="classcUnivarPolynomial.html#a936aa1a9e68b7005af72be0fbb2d91ac">sturmSequence</a>()<span class="keyword">const</span>;</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    std::vector&lt;double&gt; &amp;<a class="code" href="classcUnivarPolynomial.html#a887727886c8d9ed3a789b10de1c50785">solveRQuadratic</a>(std::vector&lt;double&gt; &amp;zeros)<span class="keyword">const</span>;</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;    std::vector&lt;double&gt;&amp; <a class="code" href="classcUnivarPolynomial.html#a9203e9c2e0c7d1f4d70c13b08e37d5ff">solveRCubic</a>(std::vector&lt;double&gt; &amp;zeros)<span class="keyword">const</span>;</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    <span class="keywordtype">int</span> <a class="code" href="classcUnivarPolynomial.html#a3faca94991f37531436883070bcc7f01">sturmSignsNo</a>(<span class="keywordtype">double</span> x0)<span class="keyword">const</span>;</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">class</span> Y&gt;</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;    <span class="keyword">friend</span> std::ostream&amp; operator&lt;&lt;(std::ostream&amp; out, const cUnivarPolynomial&lt;Y&gt;&amp; poly);</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">class</span> Y&gt;</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;    <span class="keyword">friend</span> std::ostream&amp; operator&lt;&lt;(std::ostream&amp; out, const std::pair&lt;cUnivarPolynomial&lt;Y&gt;, <a class="code" href="classcVariable.html">cVariable</a>&gt;&amp; poly);</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;    <span class="comment">//polynomial[size-1] has the highest power</span></div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;    bmt::polynomial&lt;T&gt; m_PolyImpl;</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    <span class="comment">//functor equality comparation with specified degree of accuracy</span></div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;    <span class="keyword">mutable</span> bmt::eps_tolerance&lt;T&gt; m_Tolerance;</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;};</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt;</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;<span class="keyword">inline</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a> gcd(<span class="keyword">const</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a>&amp; a, <span class="keyword">const</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a>&amp; b)</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;{</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;    <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;    <span class="comment">//TODO</span></div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;}</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt;</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;<span class="keyword">inline</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a> operator*(<span class="keyword">const</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a>&amp; a, <span class="keyword">const</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a>&amp; b)</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;{</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;    <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a> result(a);</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;    result *= b;</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;}</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt;</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;<span class="keyword">inline</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a> operator%(<span class="keyword">const</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a>&amp; a, <span class="keyword">const</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a>&amp; b)</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;{</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;    <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a> result(a);</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;    result %= b;</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;    <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;}</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt;</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;<span class="keyword">inline</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a> operator/(<span class="keyword">const</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a>&amp; a, <span class="keyword">const</span> <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a>&amp; b)</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;{</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;    <a class="code" href="classcUnivarPolynomial.html">cUnivarPolynomial&lt;T&gt;</a> result(a);</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;    result /= b;</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;    <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;}</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt;</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;<span class="keyword">inline</span> std::ostream&amp; operator&lt;&lt;(std::ostream&amp; out, const cUnivarPolynomial&lt;T&gt;&amp; poly)</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;{</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;    <span class="keywordtype">size_t</span> idx = poly.size();</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;    <span class="keywordflow">for</span>( ; idx &gt; 0; idx--)</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;    {</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;        <span class="keywordflow">if</span>(poly.m_PolyImpl[idx - 1] != 0.0)</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;        {</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;            <span class="keywordflow">if</span>(idx - 1 != poly.size() - 1)</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;                out &lt;&lt; <span class="stringliteral">&quot; + &quot;</span>;</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;            out &lt;&lt; poly.m_PolyImpl[idx - 1];</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;            <span class="keywordflow">if</span>(idx - 1 != 0)</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;                out&lt;&lt; <span class="stringliteral">&quot;x^&quot;</span> &lt;&lt; idx - 1;</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;        }</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;    }</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;    <span class="keywordflow">return</span> out;</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;}</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;<span class="comment">//print polynomial with respect to variable</span></div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt;</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;<span class="keyword">inline</span> std::ostream&amp; operator&lt;&lt;(std::ostream&amp; out, const std::pair&lt;cUnivarPolynomial&lt;T&gt;, <a class="code" href="classcVariable.html">cVariable</a>&gt;&amp; poly)</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;{</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;    <span class="keywordtype">size_t</span> idx = poly.first.size();</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;    <span class="keywordflow">for</span>( ; idx &gt; 0; idx--)</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;    {</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;        <span class="keywordflow">if</span>(poly.first.m_PolyImpl[idx - 1] != 0.0)</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;        {</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;            <span class="keywordflow">if</span>(idx - 1 != poly.first.size() - 1)</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;                out &lt;&lt; <span class="stringliteral">&quot; + &quot;</span>;</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;            out &lt;&lt; poly.first.m_PolyImpl[idx - 1];</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;            <span class="keywordflow">if</span>(idx - 1 != 0)</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;                out &lt;&lt; poly.second &lt;&lt; <span class="stringliteral">&quot;^&quot;</span> &lt;&lt; idx - 1;</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;        }</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;    }</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;    <span class="keywordflow">return</span> out;</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;}</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;</div>
<div class="ttc" id="classcUnivarPolynomial_html_a0d81e941a048c6ca649dd11d8a4cda8b"><div class="ttname"><a href="classcUnivarPolynomial.html#a0d81e941a048c6ca649dd11d8a4cda8b">cUnivarPolynomial::realZeros</a></div><div class="ttdeci">std::vector&lt; double &gt; realZeros() const </div><div class="ttdef"><b>Definition:</b> univar_polynomial.cpp:56</div></div>
<div class="ttc" id="classcUnivarPolynomial_html_a60558f674dbadb2d18e3406f4d45da0e"><div class="ttname"><a href="classcUnivarPolynomial.html#a60558f674dbadb2d18e3406f4d45da0e">cUnivarPolynomial::operator/=</a></div><div class="ttdeci">cUnivarPolynomial&lt; T &gt; &amp; operator/=(const cUnivarPolynomial &amp;poly)</div><div class="ttdef"><b>Definition:</b> univar_polynomial.cpp:248</div></div>
<div class="ttc" id="classcUnivarPolynomial_html_a9203e9c2e0c7d1f4d70c13b08e37d5ff"><div class="ttname"><a href="classcUnivarPolynomial.html#a9203e9c2e0c7d1f4d70c13b08e37d5ff">cUnivarPolynomial::solveRCubic</a></div><div class="ttdeci">std::vector&lt; double &gt; &amp; solveRCubic(std::vector&lt; double &gt; &amp;zeros) const </div><div class="ttdef"><b>Definition:</b> univar_polynomial.cpp:378</div></div>
<div class="ttc" id="classcUnivarPolynomial_html_a887727886c8d9ed3a789b10de1c50785"><div class="ttname"><a href="classcUnivarPolynomial.html#a887727886c8d9ed3a789b10de1c50785">cUnivarPolynomial::solveRQuadratic</a></div><div class="ttdeci">std::vector&lt; double &gt; &amp; solveRQuadratic(std::vector&lt; double &gt; &amp;zeros) const </div><div class="ttdef"><b>Definition:</b> univar_polynomial.cpp:344</div></div>
<div class="ttc" id="classcUnivarPolynomial_html_abd186b4aab94bf19bf33796df810785e"><div class="ttname"><a href="classcUnivarPolynomial.html#abd186b4aab94bf19bf33796df810785e">cUnivarPolynomial::plotPoints</a></div><div class="ttdeci">std::vector&lt; std::pair&lt; double, double &gt; &gt; plotPoints(double min, double max, double increment) const </div><div class="ttdef"><b>Definition:</b> univar_polynomial.cpp:133</div></div>
<div class="ttc" id="classcUnivarPolynomial_html_a936aa1a9e68b7005af72be0fbb2d91ac"><div class="ttname"><a href="classcUnivarPolynomial.html#a936aa1a9e68b7005af72be0fbb2d91ac">cUnivarPolynomial::sturmSequence</a></div><div class="ttdeci">std::vector&lt; cUnivarPolynomial&lt; T &gt; &gt; sturmSequence() const </div><div class="ttdef"><b>Definition:</b> univar_polynomial.cpp:312</div></div>
<div class="ttc" id="classcUnivarPolynomial_html_af0fa0596f636515bcab1e2dedc2fde79"><div class="ttname"><a href="classcUnivarPolynomial.html#af0fa0596f636515bcab1e2dedc2fde79">cUnivarPolynomial::derivative</a></div><div class="ttdeci">cUnivarPolynomial&lt; T &gt; derivative() const </div><div class="ttdef"><b>Definition:</b> univar_polynomial.cpp:13</div></div>
<div class="ttc" id="classcUnivarPolynomial_html"><div class="ttname"><a href="classcUnivarPolynomial.html">cUnivarPolynomial</a></div><div class="ttdef"><b>Definition:</b> univar_polynomial.h:25</div></div>
<div class="ttc" id="classcUnivarPolynomial_html_a3aeaae886ae33ff00e9207847c68deb2"><div class="ttname"><a href="classcUnivarPolynomial.html#a3aeaae886ae33ff00e9207847c68deb2">cUnivarPolynomial::operator%=</a></div><div class="ttdeci">cUnivarPolynomial&lt; T &gt; &amp; operator%=(const cUnivarPolynomial &amp;poly)</div><div class="ttdef"><b>Definition:</b> univar_polynomial.cpp:182</div></div>
<div class="ttc" id="classcUnivarPolynomial_html_a4158585d1768e886c6802030f6ec128f"><div class="ttname"><a href="classcUnivarPolynomial.html#a4158585d1768e886c6802030f6ec128f">cUnivarPolynomial::operator*=</a></div><div class="ttdeci">cUnivarPolynomial&lt; T &gt; &amp; operator*=(const cUnivarPolynomial &amp;poly)</div><div class="ttdef"><b>Definition:</b> univar_polynomial.cpp:221</div></div>
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<div class="ttc" id="classcUnivarPolynomial_html_a3faca94991f37531436883070bcc7f01"><div class="ttname"><a href="classcUnivarPolynomial.html#a3faca94991f37531436883070bcc7f01">cUnivarPolynomial::sturmSignsNo</a></div><div class="ttdeci">int sturmSignsNo(double x0) const </div><div class="ttdef"><b>Definition:</b> univar_polynomial.cpp:432</div></div>
<div class="ttc" id="classcVariable_html"><div class="ttname"><a href="classcVariable.html">cVariable</a></div><div class="ttdef"><b>Definition:</b> variable.h:7</div></div>
<div class="ttc" id="classcUnivarPolynomial_html_a651a710f52fdd21136419d2c6fef5574"><div class="ttname"><a href="classcUnivarPolynomial.html#a651a710f52fdd21136419d2c6fef5574">cUnivarPolynomial::operator()</a></div><div class="ttdeci">T operator()(const Y &amp;value) const </div><div class="ttdef"><b>Definition:</b> univar_polynomial.h:112</div></div>
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